Simplify: $ \frac{-9}{42}+\left(\frac{-5}{21}\right)+\frac{3}{84}+\frac{1}{6} $.

Given:

\( \frac{-9}{42}+\left(\frac{-5}{21}\right)+\frac{3}{84}+\frac{1}{6} \).

To do:

We have to simplify \( \frac{-9}{42}+\left(\frac{-5}{21}\right)+\frac{3}{84}+\frac{1}{6} \).
Solution:
 \( \frac{-9}{42}+\left(\frac{-5}{21}\right)+\frac{3}{84}+\frac{1}{6} \).

LCM of 42, 21, 84 and 6 $=84$.

$\frac{-9}{42}+\frac{-5}{21}+\frac{3}{84}+\frac{1}{6}=\frac{-9\times2+(-5\times4)+3\times1+1\times14}{84}$

$=\frac{-18-20+3+14}{84}$

$=\frac{-38+17}{84}$

$=\frac{-21}{84}$

$=\frac{-1}{4}$

Therefore,

$\frac{-9}{42}+\frac{-5}{21}+\frac{3}{84}+\frac{1}{6}=\frac{-1}{4}$.

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Updated on: 10-Oct-2022

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